The Scaling Limit of the (∇ + Δ) -Model

Journal article (2021)

Authors

A. Cipriani Applied Probability -

Biltu Dan Indian Statistical Institute

Rajat Subhra Hazra Indian Statistical Institute

Research Group

Applied Probability () (TU Delft)

Scaling limit Membrane model Gaussian free field Mixed model Random interface

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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

In this article we study the scaling limit of the interface model on Zd where the Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any dimension the scaling limit is given by the Gaussian free field. We discuss the appropriate spaces in which the convergence takes place. While in infinite volume the proof is based on Fourier analytic methods, in finite volume we rely on some discrete PDE techniques involving finite-difference approximation of elliptic boundary value problems.

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